Geometric modeling kit and method of making same

ABSTRACT

A geometrical structural system is made up of a plurality of nodes and shape-coded connectors extending therebetween, each node having a plurality of outer polygonal elements. The outer edges of each element are bordered by end edges of other elements and each element has an opening therethrough corresponding to the outer side edges of each element. Each opening extends radially into a hollow space centrally of each node. The connectors are elongated and have opposed connecting ends with a cross-sectional configuration corresponding to a cross-sectional configuration of an opening in one of the element faces for insertion therein. The steps involved in making the nodes includes tooling a pair of mold halves with interior cavities; fastening the halves together with the interior cavities confronting one another to form a common cavity symmetrical about their center; positioning slides in the common cavity, each slide corresponding to the cross-sectional configuratrion of a polyhedral face to be formed in the outer shell but smaller in cross-sectional size than the polyhedral face; injecting a moldable material to fill the common cavity and remaining voids between the slides; followed by withdrawing the slides from the mold cavity and disconnecting the mold halves for removal of a one-piece node.

SPECIFICATION

This invention relates to a novel and improved geometric structuralsystem, and more particularly relates to a novel and improved geometricmodeling kit and method of making same.

BACKGROUND AND FIELD OF THE INVENTION

It is customary to form geometric modeling kits or units comprised ofuniversal nodes or connectors which can be expanded into structuralnetworks by the interconnection of nodes with connecting struts orspokes. Typically, the struts are elongated with each end beinginsertable into a selected opening or cavity in a node and, by combininga series of nodes and struts together in different selected angularrelationships, numerous three-dimensional figures can be constructed.Such systems or kits have definite aesthetic and structural appeal bothfrom the standpoint of providing a geometric modeling kit or toy forpersons of all ages as well as rather sophisticated geometric structuralsystems. Representative of such approaches is that disclosed in U.S.Pat. No. 3,600,825 to P. J. Pearce in which the nodes themselves aremade up of radially extending spokes of different cross-sectionalconfigurations which are interconnected together by struts and splicemembers. The spokes and struts are both shape-coded and in some casescolor-coded to facilitate matching up or interconnection of ends ofcorresponding cross section, as further aided by the use of couplingmembers therebetween. Again, however, the node itself is a star-likerigid molded or fabricated device having spokes of variouscross-sectional configurations radiating from a common center.

Another approach is exemplified by U.S. Pat. No. 3,722,153. Baer inwhich a structural network or three-dimensional figure is formed byconnection of hall-shaped nodes or connectors and structs into differentgeometric configurations utilizing the five-fold symmetries of theicosahedron and the dodecanedron. The structural elements must beattached, such as, by welding their ends at different angles to thegeometric connectors or nodes to define the different angles of thestructural network but without the benefit of shape-coding between therespective nodes and struts.

In the past, construction of the nodes as employed in the Pearce andBaer patents has presented insurmountable problems in terms ofone-piece, high strength construction. The nodes of Baer were designedto be essentially of spherical construction, and the geometry of theball-shaped connectors as employed in Baer or the radiating spokes asemployed in Pearce virtually precluded one-piece construction ormolding.

It is therefore proposed to provide a geometric structural system havingparticular application to modeling kits or toys in which the nodes orconnectors can be formed of one-piece construction to lend the desiredstrength and unity to the system while at the same time achieve by meansof shape-coding and color-coding where desired the proper matching orinterrelationship between the connecting struts or structural elementsin the formation of different geometrical designs.

Other U.S. Letters Patent of interest are those to U.S. Pat. No.3,341,989 to D. G. Emmerich; U.S. Pat. No. 3,510,962 to L. Sato; U.S.Pat. No. 3,854,255 to R. L. Baker; U.S. Pat. No. 4,258,513 to H.Bergman; U.S. Pat. No. 4,271,628 to J. V. Barlow; and U.S. Pat. Nos.4,326,354 and 4,348,830 to C. E. Haberg; also, French Pat. No. 1,425,234to M. Marboeuf.

SUMMARY OF INVENTION

It is therefore an object of the present invention to provide for anovel and improved geometrical structural system which is specificallyadapted for use in geometrical modeling kits and to novel and improvedmethods of making same.

It is another object of the present invention to provide for a geometricmodeling kit in which the parts can be assembled together into adiversity of highly stable geometric models and/or structural networksand at the same time serve as a valuable learning tool in theconstruction of different geometric designs.

Another object of the present invention is to provide for a new andimproved universal node serving as a means of interconnection betweenstruts to form different geometrical designs ranging from simple cubesto true projections from the fourth dimension into three-space and wherethe nodes are in the form of hollow balls with shaped-coded openings tofacilitate interconnection of the struts therebetween in a user-friendlymanner.

A further object of the present invention is to provide for a novel andimproved method of molding hollow novel or connectors for a geometricmodeling kit which permits one-piece construction of the nodes whileeliminating secondary finishing operations and achieves shape-coding forthe purpose of facilitating connection of struts between adjacent nodes.

An additional object of the present invention is to provide for a noveland improved combination of structural elements and nodes which combinesthe desired characteristics of shape-coding with sophisticatedgeometrical configurations for applications ranging from modeling kitsor toys to high strength structural systems.

In accordance with the present invention, a geometrical structuralsystem has been devised which is made up of a plurality of nodes andshape-coded connectors extending between the nodes, each node having aplurality of outer polyhedral elements with outer edges of each elementbordered by end edges of other elements, each element having an openingtherethrough corresponding in configuration to outer side edges of eachelement, each opening extending radially into communication with ahollow space centrally of each node. The struts are elongated and haveopposed connecting ends, each connecting end having a cross-sectionalconfiguration corresponding to a cross-sectional configuration of anopening in one of the faces of an element for insertion therein.

In a preferred embodiment, each node is in the form of arhombicosidodecahedron having a plurality of flat pentagonal faces withoutside edges of each pentagonal face bordered by end edges ofrectangular faces, and opposed edges of each rectangular face borderedby side edges of a triangular face, each face having an openingtherethrough which corresponds in configuration to the outer side edgesof a face, each opening extending radially toward the center of eachnode, there being a plurality of struts or sticks having opposedconnecting ends with cross-sectional configurations corresponding to thedifferent cross-sectional configurations of the openings in the facesfor selected insertion therein. Further, the struts are of selectedlengths according to the cross-sectional configurations of theirconnecting ends so as to form a multiplicity of three-dimensionalfigures of various geometric designs in space.

Both the nodes and struts as formed in accordance with the presentinvention may be injection molded of plastic, rubber or rubber-likematerials depending upon the degree of strength and rigidity desired.Most desirably, the material composition of the nodes as well as thesticks is a moldable material which is inert or non-toxic, impact proofand highly stable under different environmental conditions. In apreferred method of making the nodes of the present invention, a pair ofmold halves are tooled or machined, each half including an interiorcavity area, fastening the mold halves together with the interiorcavities in confronting relation to one another to form a common cavitysymmetical about the center of the mold halves, positioning slides inthe common cavity formed between the connected mold halves, each slidecorresponding to the cross-sectional configuration of a polyhedral faceto be formed in the outer shell of the mold but of a smallercross-sectional size than the polyhedral face, injecting a moldablematerial into the mold to fill the common cavity and remaining voidsbetween the slides and curing said material in the mold, and followed bywithdrawing the slides from the mold cavity and disconnecting the moldhalves for removal of a finished, one-piece node therefrom. By insertingthe slides through different shaped openings in the mold halves so as toextend along radial lines, it is possible to form nodes of differentgeometrical configurations and with different shaped polyhedral faceswhich are provided with shape-coded openings in each polyhedral facewhich are adapted for insertion of correspondingly shape-coded struts ofdifferent geometric configuration.

The above and other objects, advantages and features of the presentinvention will become more readily appreciated and understood from aconsideration of the following detailed description of a preferredembodiment of the present invention when taken together with theaccompanying drawings of a preferred embodiment of the presentinvention, in which:

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a front view in elevation of a preferred form of node inaccordance with the present invention;

FIG. 2 is a cross-sectional view taken about lines 2--2 of FIG. 1;

FIG. 3 is a front view in elevation of a structural element havingopposed connecting ends for insertion in triangular faces of the nodes;

FIG. 4 is an end view of one connecting end of the structural elementshown in FIG. 3;

FIG. 5 is an end view of the opposite connecting end of the structuralconnecting element shown in FIG. 3;

FIG. 6 is a front view in elevation of a pentagonal structural element;

FIGS. 7 and 8 are end views of opposed connecting ends of the structuralelement shown in FIG. 6;

FIG. 9 is a front view in elevation of a structural element havingrectangular connecting ends;

FIG. 10 is an end view of one of the opposed connecting ends of thestructural elements shown in FIG. 9;

FIG. 11 is a somewhat perspective view illustrating interconnection ofthe structural elements of the type shown in FIGS. 3 and 9 into a node;

FIG. 12 is a perspective view illustrating a three-dimensionalstructural network comprised of the preferred forms of nodes andstructural elements;

FIG. 13 is a somewhat schematic view illustrating the steps to befollowed in the fabrication of a simple shape-coded node in the form ofa cube in accordance with the present invention;

FIG. 14 is an exploded view of a mold employed in making arhombicosidodecahedron node; and

FIG. 15 is a perspective view of a star polyhedron.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

Referring to FIGS. 12 and 15, there is shown by way of illustrativeexample assembled elements of a geometric model toy kit which arecomprised of correspondingly shaped nodes 10 assembled by means ofstruts generally designated at 12, 12' and 12" into a three-dimensionalfigure. In FIG. 12, each node 10 is in the form of arhombicosidodecahedron which, as shown in FIGS. 1 and 2, consists ofthirty rectangular elements 14, twenty triangular elements 16 and twelvepentagonal elements 18.

Considering in more detail the makeup of the individual elements 14, 16and 18, it will be noted that the elements are arranged together to forman open shell with a central or inner cavity as designed at 20. Eachelement 14, 16 and 18 has a radially extending opening designated 14',16' and 18', respectively, corresponding to the configuration of thatelement, each opening converging radially and inwardly toward the centerof the node. The rectangular elements 14 have inner edges 24 whichsurround its opening, the triangular elements 16 have edges 26 and thepentagonal elements 18 are bordered by edges 28. Moreover, the elements14, 16 and 18 have external end faces 30, 31 and 32, respectively, whichmake up the external surface of the node. Each end face is interruptedby the openings 14', 16' and 18' at their inner edges as described andby outer edges 34, 36 and 38, respectively. In therhombicosidodecahedron as shown, the pentagonal connecting ends 18 arebordered by shorter edges of the rectangular faces 14, and opposedlonger edges of the rhombic faces are bordered by side edges of atriangular face 16, the nodes being symmetrically formed about animaginary vertical plane passing through its center, for example, asrepresented by the section line 2--2 of FIG. 1.

As shown in FIGS. 3 to 10, each structural element or strut 12, 12' and12" is correspondingly comprised of an elongated body 46, 46' and 46"having opposed connecting ends 48, 48' and 48", the ends 48 beingshape-coded to correspond to the cross-sectional configuration and sizeof the openings of the respective elements 14, 16 and 18 of the node.Thus, by reference to FIG. 3, there is illustrated a triangular strut 12which corresponds to triangular elements 16 in FIG. 1 in the sense thatopposed connecting ends are of triangular cross-section as shown in FIG.4 and 5. Each connecting end 48 is domensioned so as to be of slightlyreduced cross section to that of the main body 46 and is sized forclose-fitting insertion into one of the triangular end faces. Further,as noted from the comparison of FIGS. 4 and 5, the main body 46 isrotated 180° so that one connecting end is displaced 180° from the otherto define what is termed as an antiprism. In the preferred embodiment,this is achieved by forming the main body with two end sections 49 and50 but displaced 180° with respect to one another by a commonintermediate section 52 and where, for example, a flat side of an outersection tapers along the intermediate section into a vertex at the otherouter section. In FIG. 6, again opposed connecting ends 48' aredisplaced 180° with respect to one another, as seen from a comparison ofFIGS. 7 and 8, by displacement of outer sections 53 and 54 through 180°via intermediate section 55. In the form of FIGS. 6 to 8, the pentagonalconnecting ends 48' are configured and sized for close-fitting insertioninto the pentagonal end faces 32.

In FIG. 9, opposed connecting ends 48" are joined by a common or mainelongated body 46" which is similarly of rectangular cross-sectionalconfiguration but not rotated through 180°.

In the preferred form, the relative lengths of the structural elementsare governed by the divine proportion: T=√5/2+1/2≅1.61804. Thus, therectangular struts 12" are preferably T powers of a unit length, thetriangular struts or elements 12 are T powers of the cosine of 30+ timesthe unit length and the pentagonal struts or elements 12' are T powersof the cosine of 18° times the unit length. In dimensional geometry, therectangular, triangular and pentagonal elements correspond to thenumbers 1, 3 and 5, respectively so as to establish the properrelationship between the shape and intended function of each strut inassembling into different three-dimensional figures. This can be bestappreciated from a consideration of the assembly of the structuralelements and nodes into a three-dimensional figure as illustrated inFIGS. 12 and 15. Thus, the elements 12, 12' and 12" when assembled havetheir connecting ends inserted into the openings of the node elements14, 16 and 18 with the ends of the main body 46 abutting the end facesof the elements. The rectangular sticks define a cube in this case; thetriangular sticks define a rhombic dodecahedron. Other lengths of sticksare possible by using lower or higher powers of T which distances aremeasured from node centers so that the actual length of a stick fromnode face to node face equals the center to center distance minus onenode diameter.

In the preferred form, where the nodes are formed in the shape of alesser rhombicosidodecahedron, three basic forms and lengths of stickare employed to correspond to the shape of the polyhedral faces of thenode. In addition, the sticks must be dimensioned in length at a powerof T, for example, in building a structural network or three-dimensionalfigure as shown in FIGS. 12 and 15. From FIGS. 3 to 10, it will befurther noted that the bodies of the sticks are either prisms orantiprisms. Thus, the body of the rectangular stick, with an even numberof sides, is a rectangular prism. However, the bodies of the triangularand pentagonal sticks, with odd numbers of sides, are triangular andpentagonal antiprisms, respectively, since the corresponding faces 31 tobe interconnected from one node to the next are rotated 180° as can beseen from opposite faces on the same node. In this relation, selectionof the rhombicosidodecahedron merely highlights the advantages andfeatures of the present invention in forming different geometricstructures or designs through the combined utilization of the hollownodes 10 as described with interconnecting struts 12 that areshape-coded as well as length-coded to permit construction of thedesigns in a foolproof manner. Thus, the system serves as a valuablelearning tool in providing anyone with an intuitive grasp of thestructure of space. Furthermore, the geometric considerations involvinga rhombicosidodecahedron when combined with the construction of thehollow nodes 10 as described leads to a visually balanced ball and stickconstruction. For example, once the ball diameter and basic stick lengthof the rectangular stick are established, all other dimensions can bereadily determined as represented by the following Table:

                  TABLE I                                                         ______________________________________                                        No.       Shape      Length                                                   ______________________________________                                        1         rectangle  (unity) (T.sup.n )-node diameter                         3         triangle   (cos 30°) (T.sup.n )-node diameter                5         pentagon   (cos 18°) (T.sup.n )-node diameter                ______________________________________                                    

In forming the sticks in the manner described with the connecting endsof reduced size with respect to the body, the shoulder surfaces formedat the ends of the body permit the sticks to contact a greater area whenthe connecting ends are inserted into the hollow faces of the nodes andthus stabilize the entire construction of the toy.

The rhombic dodeahedron of FIG. 2 is a subset of the body centered cubiclattice. On the other hand, a regular dodecahedron defines five uniquecubic lattices in space, thus defining five unique rhombic dodecahedraall centered on the same coordinate origin. Moreover, the regulardodecahedron can be stellated and then "squashed" along its three-foldaxis of symmetry; that is, in the unit cube defined by the dodecahedronwith all faces perpendicular to the coordinate axes, a line from point1/2, 1/2, 1/2 to -1/2, -1/2, -1/2 is shortened from √3 to √3/2. Thisresults in the view shown in FIG. 15 wherein all three of the struts 12,12' and 12" are used to interconnect a series of nodes 10 in the mannershown. The interrelationship between FIGS. 12 and 15 helps to illuminatethe diversity of models possible with the preferred embodiment of theinvention.

A molding sequence in accordance with the present invention isschematically illustrated in FIG. 13 for the manufacture of a hollowcubic node. As illustrated in FIG. 13A, a pair of mold halves 60 arepositioned in confronting relation to one another, each half includingan interior mold surface 62 corresponding to the configuration of theexternal configuration of one-half of each node. Slide or plungerelements 64 are positioned in radial openings 65 in each mold half.

As illustrated in FIG. 13B, the mold halves are clamped together in asuitable press, not shown, and the movable slides 64 are advanced intothe mold until they abut one another at the center of the mold asillustrated in FIG. 13C. Each slide 64 is shape-coded to correspond tothe desired cross-sectional configuration of the opening in the elementof the finished node and, for example, is of square or rectangularcross-section for the cubic node shown. Further, the leading ends of theslides are tapered as represented at 66 with complementary angles toadvance into flush relationship to adjacent slides, thus forming boththe openings and the void space in the center of the node. In otherwords, the slides are elongated prisms of the holes or openings whichthey will form, and the cross-section of each prism is a proportionalreduction of the end face or element in which the opening is formed.Preferably, the ends 66 of the slides 64 are tapered such that they addup to the dihedral angle between their corresponding polygon faces so asto allow the slides to abut together and to form a common void space inthe shape and orientation of the original polyhedron, only smaller, atthe center of the node.

Once so positioned as illustrated in FIG. 13C, hot plastic asrepresented at P is injected into the mold so as to fill the remainingnetwork between the mold cavity and slides. Once the plastic is cured,the slides 64 are withdrawn as illustrated in FIG. 13D and the finishednode is then withdrawn from the mold in one piece as illustrated in FIG.13E.

There is illustrated in FIG. 14 a pair of mold halves for making therhombicosidodecahedral node as illustrated in FIG. 12 and wherein likeparts to those of FIG. 13 are correspondingly enumerated. In the uppermold half, it will be noted that the slides are in their retractedposition, but in the left mold half the slides are shown projectedinwardly into abutting relation. Moreover, the mold halves are notcompletely symmetrical and are configured along with mating portions ofthe halves such that the slides are fully supported in one side or theother of a mold half. For example, the rectangular area designated at 70in the left mold half as well as the triangular areas 72 serve to fullysupport the slides for forming the elements along the midsection of thenodes. Accordingly, the mold halves are formed in complementary, matingend surfaces and need not necessarily be flat or flush end surfaces asillustrated in the formation of the cubic node in FIG. 13. In the morecomplex form of molding process, the tapered ends 66 of the slides abutone another just inwardly of the interior of the mold and therebyeffectively seal off the entire mold cavity from the entry of moldablematerial. In other words, it is not necessary for the tapered ends ofthe slides to occupy the entire interior space. Most desirably, thematerial composition of the nodes as well as the sticks is a moldablematerial which is inert or non-toxic, impact proof and highly stableunder different environmental conditions.

Accordingly, the method of the present invention enables injectionmolding of complex shape-coded nodes of one-piece construction in whichthe resultant polyhedrons are formed with openings of the same shape asthe polygon in which they extend. It should be noted both with respectto the forms of FIGS. 13 and 14 that the slides 64 are regular prismsbut are tapered at their ends to advance into flush abutting relation toadjacent slides as illustrated in the right mold half. In this respect,the slides are arranged to form the radial openings 14', 16' and 18' ineach of the polygons formed, as illustrated in FIG. 1.

It will be evident from the foregoing description of the preferred formof structural system described as well as the method for making samethat the present invention has useful application not only in geometricmodeling kits but to space frame structures and designs as well. While apreferred form is described in connection with the formation ofrhombicosidodecahedral nodes, the principles thereof have utility inother geometric designs. Further, the relative lengths of sticksemployed may be varied in accordance with the type of geometric designsdesired.

It is therefore to be understood that various other modifications andchanges may be made in the construction and design of systems as hereindescribed without departing from the spirit and scope of the presentinvention as defined by the appended claims.

We claim:
 1. A geometrical device comprising a plurality of hollow nodes and shape-coded connectors extending between said nodes, said nodes and connectors assembled into a three-dimensional, geometric figure, each node having a plurality of polygonal elements consisting of a combination of triangular, rectangular and pentagonal elements with outside edges of each polygonal element bordered by edges of adjacent polygonal elements, each element having an opening therethrough corresponding in configuration to outer side edges of each said element with each opening converging radially toward the center of each node; andsaid plurality of connectors being elongated and having opposed connecting ends, each connecting end having a cross-sectional configuration corresponding to a cross-sectional configuration of an opening in one of said elements for insertion therein, the relative lengths of said connectors .[.based on on T.]. .Iadd.having rectangular connecting ends .Iaddend.powers of unity where T=√5/2+1/2.
 2. In a geometrical unit according to claim 1, each said polygonal element having a flat external face.
 3. In a geometrical unit according to claim 1, opposed connecting end of each said connector having corresponding cross-sectional configurations.
 4. In a geometrical unit according to claim 1, a connecting end of each said connector being rotated 180° from the opposite connecting end of said connector.
 5. In a geometrical unit according to claim 4, at least selected of said connectors having a main body comprised of elongated triangular sections extending between opposed connecting ends.
 6. In a geometrical unit according to claim 5, wherein adjacent of said triangular sections extend in opposite directions to one another.
 7. A geometrical unit comprising a plurality of hollow nodes and shape-coded connectors extending between said nodes, said nodes and connectors assembled into a three-dimensional figure, each node being in the form of a rhombicosidodecahedron having a plurality of flat pentagonal faces with outside edges of each pentagonal face bordered by shorter edges of rectangular face and longer side edges of each rectangulars, face bordered by side edges of a triangular face, each face having an opening therethrough corresponding in configuration to outer edges of said face, each opening extending radially toward the center of each node, and said plurality of connectors being elongated and having opposed connecting ends, each connecting end having a cross-sectional configuration corresponding to a cross-sectional configuration of an opening in one of said faces for insertion therein.
 8. In a geometrical unit according to claim 7, opposite connecting ends of each said connector having a corresponding cross-sectional configuration.
 9. In a geometrical unit according to claim 7, a connecting end of each said connector being rotated 180° from the opposite connecting end of said connector.
 10. In a geometrical unit according to claim 7, each of said openings converging radially inwardly toward the center of each said node. .Iadd.11. A geometrical device according to claim 1, the relative lengths of said connectors having triangular connecting ends based on T powers of the cosine of 30° and the relative lengths of the connectors having pentagonal connecting ends based on T powers of the cosine of 18° times the unit length. .Iaddend. 